PKU 2584 - T-Shirt Gumbo (二分图最大匹配 & 匈牙利算法 | 最大流 & EK)

题意

给出一个人能穿的型号和每个型号衣服的多少，求能不能每个人恰好分配到一件。

思路

第一次先用最大流写了一下，然后就试试最大匹配。

最大匹配就是把n件相同的衣服拆成一件一件，分别编号，再把人和它们相连，然后就匈牙利算法了。 
感觉用最大匹配写繁琐一点。

被注释部分是最大流的

代码

  
  
  
  

   
   
   
   
#include <cstdio>
   
   
   
   
#include <stack>
   
   
   
   
#include <set>
   
   
   
   
#include <iostream>
   
   
   
   
#include <string>
   
   
   
   
#include <vector>
   
   
   
   
#include <queue>
   
   
   
   
#include <functional>
   
   
   
   
#include <cstring>
   
   
   
   
#include <algorithm>
   
   
   
   
#include <cctype>
   
   
   
   
#include <string>
   
   
   
   
#include <map>
   
   
   
   
#include <cmath>
   
   
   
   
#define LL long long
   
   
   
   
#define SZ(x) (int)x.size()
   
   
   
   
#define Lowbit(x) ((x) & (-x))
   
   
   
   
#define MP(a, b) make_pair(a, b)
   
   
   
   
#define MS(arr, num) memset(arr, num, sizeof(arr))
   
   
   
   
#define PB push_back
   
   
   
   
#define F first
   
   
   
   
#define S second
   
   
   
   
#define ROP freopen("input.txt", "r", stdin);
   
   
   
   
#define MID(a, b) (a + ((b - a) >> 1))
   
   
   
   
#define LC rt << 1, l, mid
   
   
   
   
#define RC rt << 1|1, mid + 1, r
   
   
   
   
#define LRT rt << 1
   
   
   
   
#define RRT rt << 1|1
   
   
   
   
#define BitCount(x) __builtin_popcount(x)
   
   
   
   
const double PI = acos(-1.0);
   
   
   
   
const int INF = 0x3f3f3f3f;
   
   
   
   
using namespace std;
   
   
   
   
const int MAXN = 100 + 10;
   
   
   
   
const int MOD = 1e9 + 7;
   
   
   
   
const int dir[][2] = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
   
   
   
   

   
   
   
   
typedef pair<int, int> pii;
   
   
   
   
typedef vector<int>::iterator viti;
   
   
   
   
typedef vector<pii>::iterator vitii;
   
   
   
   

   
   
   
   
string str = "0SMLXT";
   
   
   
   

   
   
   
   
struct EDGES
   
   
   
   
{
   
   
   
   
 int from, to;
   
   
   
   
};
   
   
   
   

   
   
   
   
struct EDGE
   
   
   
   
{
   
   
   
   
 int from, to, cap, flow;
   
   
   
   
};
   
   
   
   

   
   
   
   
int start[6], cnt[6], L[MAXN], R[MAXN];
   
   
   
   
int link[MAXN], vis[MAXN], head[MAXN], next[MAXN * MAXN];
   
   
   
   

   
   
   
   
struct BIMATCHING
   
   
   
   
{
   
   
   
   

   
   
   
   
 vector<EDGES> edges;
   
   
   
   

   
   
   
   
 void init()
   
   
   
   
 {
   
   
   
   
 MS(link, -1); MS(head, -1);
   
   
   
   
 edges.clear();
   
   
   
   
 }
   
   
   
   

   
   
   
   
 void add_edge(int from, int to)
   
   
   
   
 {
   
   
   
   
 edges.PB((EDGES){from, to});
   
   
   
   
 int m = SZ(edges);
   
   
   
   
 next[m - 1] = head[from];
   
   
   
   
 head[from] = m - 1;
   
   
   
   
 }
   
   
   
   

   
   
   
   
 bool dfs(int u)
   
   
   
   
 {
   
   
   
   
 for (int i = head[u]; i != -1; i = next[i])
   
   
   
   
 {
   
   
   
   
 EDGES &e = edges[i];
   
   
   
   
 int v = e.to;
   
   
   
   
 if (!vis[v])
   
   
   
   
 {
   
   
   
   
 vis[v] = 1;
   
   
   
   
 if (link[v] == -1 || dfs(link[v]))
   
   
   
   
 {
   
   
   
   
 link[v] = u;
   
   
   
   
 return true;
   
   
   
   
 }
   
   
   
   
 }
   
   
   
   
 }
   
   
   
   
 return false;
   
   
   
   
 }
   
   
   
   

   
   
   
   
 int hungary(int n)
   
   
   
   
 {
   
   
   
   
 int res = 0;
   
   
   
   
 for (int i = 6; i < 6 + n; i++)
   
   
   
   
 {
   
   
   
   
 MS(vis, 0);
   
   
   
   
 if (dfs(i)) res++;
   
   
   
   
 }
   
   
   
   
 return res;
   
   
   
   
 }
   
   
   
   
}hun;
   
   
   
   

   
   
   
   
/*
   
   
   
   

   
   
   
   
struct MAXFLOW
   
   
   
   
{
   
   
   
   
 int head[MAXN], next[MAXN * MAXN], N, a[MAXN], p[MAXN];
   
   
   
   
 vector<EDGE> edges;
   
   
   
   

   
   
   
   
 void init(int N)
   
   
   
   
 {
   
   
   
   
 this->N = N;
   
   
   
   
 MS(head, -1);
   
   
   
   
 edges.clear();
   
   
   
   
 }
   
   
   
   

   
   
   
   
 void add_edge(int from, int to, int cap)
   
   
   
   
 {
   
   
   
   
 edges.PB((EDGE){from, to, cap, 0});
   
   
   
   
 edges.PB((EDGE){to, from, 0, 0});
   
   
   
   
 int m = SZ(edges);
   
   
   
   
 next[m - 2] = head[from];
   
   
   
   
 head[from] = m - 2;
   
   
   
   
 next[m - 1] = head[to];
   
   
   
   
 head[to] = m - 1;
   
   
   
   
 }
   
   
   
   

   
   
   
   
 void EK(int st, int &flow)
   
   
   
   
 {
   
   
   
   
 queue<int> qu;
   
   
   
   
 while (true)
   
   
   
   
 {
   
   
   
   
 MS(a, 0);
   
   
   
   
 a[0] = INF;
   
   
   
   
 qu.push(st);
   
   
   
   
 while (!qu.empty())
   
   
   
   
 {
   
   
   
   
 int u = qu.front(); qu.pop();
   
   
   
   
 for (int i = head[u]; i != -1; i = next[i])
   
   
   
   
 {
   
   
   
   
 EDGE &e = edges[i];
   
   
   
   
 if (!a[e.to] && e.cap > e.flow)
   
   
   
   
 {
   
   
   
   
 a[e.to] = min(a[u], e.cap - e.flow);
   
   
   
   
 qu.push(e.to);
   
   
   
   
 p[e.to] = i;
   
   
   
   
 }
   
   
   
   
 }
   
   
   
   
 }
   
   
   
   
 if (!a[N]) break;
   
   
   
   
 int u = N;
   
   
   
   
 while (u != st)
   
   
   
   
 {
   
   
   
   
 edges[p[u]].flow += a[N];
   
   
   
   
 edges[p[u] ^ 1].flow -= a[N];
   
   
   
   
 u = edges[p[u]].from;
   
   
   
   
 }
   
   
   
   
 flow += a[N];
   
   
   
   
 }
   
   
   
   
 }
   
   
   
   
}maxFlow;
   
   
   
   

   
   
   
   
*/
   
   
   
   

   
   
   
   
int main()
   
   
   
   
{
   
   
   
   
 //ROP;
   
   
   
   
 string cmd;
   
   
   
   
 int i, j;
   
   
   
   
 while (cin >> cmd && cmd != "ENDOFINPUT")
   
   
   
   
 {
   
   
   
   
 int n;
   
   
   
   
 cin >> n;
   
   
   
   
 //int N = n + 5 + 1;
   
   
   
   
 //maxFlow.init(N);
   
   
   
   
 hun.init();
   
   
   
   
 string sz;
   
   
   
   
 for (i = 6; i <= n + 5; i++)
   
   
   
   
 {
   
   
   
   
 cin >> sz;
   
   
   
   
 int l = str.find(sz[0]);
   
   
   
   
 int r = str.find(sz[1]);
   
   
   
   
 L[i] = l, R[i] = r;
   
   
   
   
 /*
   
   
   
   
 for (j = l; j <= r; j++) maxFlow.add_edge(j, i, 1);
   
   
   
   
 maxFlow.add_edge(i, N, 1);
   
   
   
   
 */
   
   
   
   
 }
   
   
   
   
 int sum = 0;
   
   
   
   
 for (i = 1; i <= 5; i++)
   
   
   
   
 {
   
   
   
   
 int num;
   
   
   
   
 cin >> num;
   
   
   
   
 start[i] = sum + 1;
   
   
   
   
 cnt[i] = num;
   
   
   
   
 sum += cnt[i];
   
   
   
   
 //maxFlow.add_edge(0, i, num);
   
   
   
   
 }
   
   
   
   
 for (i = 6; i < 6 + n; i++)
   
   
   
   
 for (j = start[L[i]]; j < start[R[i]] + cnt[R[i]]; j++) hun.add_edge(i, j);
   
   
   
   
 cin >> cmd;
   
   
   
   
 int flow = hun.hungary(n);
   
   
   
   
 //maxFlow.EK(0, flow);
   
   
   
   
 printf("%s\n", (flow == n ? "T-shirts rock!" : "I'd rather not wear a shirt anyway..."));
   
   
   
   
 }
   
   
   
   
 return 0;
   
   
   
   
}